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Transcription

1 U MS ILE, LOPS 'i44 *nrd 2EPM SEON MAY IN 4A'" 2 a" wotw orgl dov4/sm oeme ru t vo lsiw ffw-tth At.a41m Aw21 m.p 8l fli4v

2 OPTIMISATION OF THE THERMOELECTRIC FIGURE OF MERIT OF MODIFIED SILICON GERMANIUM ALLOYS 1. Introduction 0o -_-n this report a working theoretical model for the power factor (cq CfL silicon germanium alloys is presented and the dependence of this parameter on carrier concentration and number of valleys explored. 2. Outline of theoretical model " 'Although silicon-germanium alloys cannot be described as narrow band gap semiconductors, the high level of doping employed in thermoelectric applications necessitates the inclusion in the theoretical model of deviations from the usually assumed parabolic bands, Non-parabolicity of the bands is usually represented in terms of a parameter 13 = k 8 3T/Eg i where ks is Boltzmann constant, T the absolute temperature and E g the energy band cap. The electrical transport properties are expressed in terms of the gcncralised Fermi integrals defined by:- nlm= Jn~(?(j+0.7?),].dn n "n 0 where f is the usual Fermi distribution, r? = E/k 0 3T is the reduced carrier energy n, m and I are numbers which take different values for various parameters and scattering mechanisms. At room temperature and above, acoustic phonon scattering is the most important carrier scattering mechanism. In the initial model intervalley scattering (IVS) has been neglected. This is a reasonable approximation as IVS involves high energy phonons which are excited only at high temperatures. The Seebeck coefficient is given by: k13 e 1 where 6 = L 1 / 1 L mrds k0t ]/20 '2 3/ and the carrier concentration n = N v u h

3 where mds is the density of states effective mass for a single valley, and Nv, the number of valleys. The reduced electrical conductivity defined by a = e j is given by a' = -- J N v O4V (T 13,72 f 2-2 (nc *XL) Various terms have their usual meanings. The electrical power factor is given by: kj 2hCt t Nv k2h L' (6- t) 3n 2 E 12 mc -2 values for various parameters employed in the calculations are given in Table I Table 1 Eg(eV) Mc/n O c (Nm - 2 ) e (ev) L(Wn-ldeg-) i x Results "-The dependence of the Seebeck coefficient ()0, electrical conductivity (' and the power factor (,jd) on carrier concentration and number of valleys N are presented. in figures Conclusions.-- / w'wo main conclusions can be drawn from the reported results A large number of equi-energetic valleys give rise to a higher power factor at room temperature, when intervalley scattering can be considered negligibly small. -<2r Higher doping levels are required in order to take advantage of the large number of valleys. -.. COpmy. j: -.,'! IN1 Av'.1 itv Codes _ t " ;-I- -, ial, i dl/o r- -es liy Q Icr.

4 5 General Conclusion A working theoretical model has been developed for silicon-germainium alloys and employed in investigating the dependence of the power factor on carrier concentration and number of valleys. The effect of intervalley scattering should be taken into account if Nv is large, even at room temperature. At higher temperatures, both intra- and intervalley scattering should be considered. The theoretical model will be refined to take these factors into consideration, and the analyses cxtended to explore the dependence of the power factor on alloy composition. D M Rowe I

5 Ge0.30Si K Nv : " n (m - 3 ) Figure 1 Variation of a with carrier concentration and number of valleys

6 T 300 K Nv: 1-10 Ge Sio E b 4 t n (m 3 ) -- Figure 2 Variation of c' with carrier concentration and number of valleys

7 NW 70 C 3 01 E b Nv Figure 3 Variation orf c 2 o with carrier concentration and number of valleys

8 T 300 K x Nv Figure 4 Variation of a' with number of valleys

9 'A to -' K E 30 =l1 m-4,o " -350 E o b/ N v Figure 5 Variation of a 2 o and a with number of valleys